1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dybincka [34]
3 years ago
13

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well

as on the accuracy and completeness of your results and explanations.
Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his score on one particular hole, known as the Water Hole.

Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Let the random variable X represent Miguel’s score on the Water Hole. In golf, lower scores are better.

(a) Suppose one of Miguel’s scores from the Water Hole is selected at random. What is the probability that Miguel’s score on the Water Hole is at most 5 ? Show your work.

(b) Calculate and interpret the expected value of X . Show your work.
(d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score? Explain your reasoning.
Mathematics
1 answer:
Aleks04 [339]3 years ago
6 0

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his score on one particular hole, known as the Water Hole.  

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Let the random variable X represent Miguel’s score on the Water Hole. In golf, lower scores are better.

(a) Suppose one of Miguel’s scores from the Water Hole is selected at random. What is the probability that Miguel’s score on the Water Hole is at most 5 ? Show your work.

(b) Calculate and interpret the expected value of X . Show your work.

A potential issue with the long hit is that the ball might land in the water, which is not a good outcome. Miguel thinks that if the long hit is successful, his expected value improves to 4.2. However, if the long hit fails and the ball lands in the water, his expected value would be worse and increases to 5.4.

c) Suppose the probability of a successful long hit is 0.4. Which approach, the short hit or long hit, is better in terms of improving the expected value of the score?

(d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score? Explain your reasoning.

Answer:

a) 80%

b) 4.55

c) 4.92

d) P > 0.7083

Step-by-step explanation:

Score  |   Probability

3          |      0.15

4          |      0.40

5          |      0.25

6          |      0.15

7          |      0.05

Let the random variable X represents Miguel’s score on the Water Hole.

a) What is the probability that Miguel’s score on the Water Hole is at most 5 ?

At most 5 means scores which are equal or less than 5

P(at most 5) = P(X ≤ 5) = P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = 0.15 + 0.40 + 0.25

P(X ≤ 5) = 0.80

P(X ≤ 5) = 80%

Therefore, there is 80% chance that Miguel’s score on the Water Hole is at most 5.

(b) Calculate and interpret the expected value of X.

The expected value of random variable X is given by

E(X) = X₃P₃ + X₄P₄ + X₅P₅ + X₆P₆ + X₇P₇

E(X) = 3*0.15 + 4*0.40 + 5*0.25 + 6*0.15 + 7*0.05

E(X) = 0.45 + 1.6 + 1.25 + 0.9 + 0.35

E(X) = 4.55

Therefore, the expected value of 4.55 represents the average score of Miguel.

c) Suppose the probability of a successful long hit is 0.4. Which approach, the short hit or long hit, is better in terms of improving the expected value of the score?

The probability of a successful long hit is given by

P(Successful) = 0.40

The probability of a unsuccessful long hit is given by

P(Unsuccessful) = 1 - P(Successful)

P(Unsuccessful) = 1 - 0.40

P(Unsuccessful) = 0.60

The expected value of successful long hit is given by

E(Successful) = 4.2

The expected value of Unsuccessful long hit is given by

E(Unsuccessful) = 5.4

So, the expected value of long hit is,

E(long hit) = P(Successful)*E(Successful) + P(Unsuccessful)*E(Unsuccessful)

E(long hit) = 0.40*4.2 + 0.60*5.4

E(long hit) = 1.68 + 3.24

E(long hit) = 4.92

Since the expected value of long hit is 4.92 which is greater than the value of short hit obtained in part b that is 4.55, therefore, it is better to go for short hit rather than for long hit. (Note: lower expected score is better)

d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score?

The expected value of long hit is given by

E(long hit) = P(Successful)*E(Successful) + P(Unsuccessful)*E(Unsuccessful)

E(long hit) = P*4.2 + (1 - P)*5.4

We want to find the probability P that will make the long hit better than short hit

P*4.2 + (1 - P)*5.4 < 4.55

4.2P + 5.4 - 5.4P < 4.55

-1.2P + 5.4 < 4.55

-1.2P < -0.85

multiply both sides by -1

1.2P > 0.85

P > 0.85/1.2

P > 0.7083

Therefore, the probability of long hit must be greater than 0.7083 that will make the long hit better than the short hit in terms of improving the expected value of the score.

You might be interested in
Monica is a lawyer who earns $8,322.65 every month. She spends $830.98 on rent, $210.36 on food, and $120.45 on gas every month.
dolphi86 [110]

Answer:

Money left from her earning after expenses is $ 7160.86

Step-by-step explanation:

Money earned by Monica every month = $ 8322.65

Money spend on rent = $ 830.98

Money spend on food = $ 210.36

Money spend on gas every month = $ 120.45

Money left from her earning = 8322.65 - ( 830.98 + 210.36 + 120.45 )

                                              = 8322.65 - 1161.79

                                              = $ 7160.86

3 0
3 years ago
Read 2 more answers
Please I am on a timer
Mila [183]

Answer: g=5

Step-by-step explanation:

4 0
2 years ago
Easton bought 8 chicken wings for $8.80. How much would it cost for 17 wings?
olga2289 [7]
18.70
Because they are 1.10 each
4 0
3 years ago
A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is label
JulijaS [17]

The growth factor of the exponential function represented by the table is 5.

The correct option is c.

<h3>What is the growth factor of the exponential function?</h3>

The growth factor of the exponential function is the ratio of the two consecutive terms (y-values).

The growth factor of the exponential function is given by;

\rm Growth\ factor=\dfrac{y(x_2)}{y(x_1)}\\\\

As per given, we have a table;

x         y

-2     0.004

-1       0.02

0       0.1

1        0.5

The value  \rm x_2 is -2 and \rm x_1 is -1.

Therefore,

the growth factor of the exponential function represented by the table would be :

\rm Growth\ factor=\dfrac{y(x_2)}{y(x_1)}\\\ \rm Growth\ factor=\dfrac{y(-1)}{y(-2)}\\\\\rm Growth\ factor=\dfrac{0.02}{0.004}\\\\ \rm Growth\ factor=5

Hence, the growth factor of the exponential function represented by the table is 5.

To know more about the Growth factor click the link given below.

brainly.com/question/985668

6 0
2 years ago
Two birds are sitting on the ground below their nest. Bird A is between the nest and Bird B. The angle of elevation from Bird A
ruslelena [56]

Answer:

Not sure

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Find the sales tax on the suit which is sold for $490.50, if the tax is 8%
    6·1 answer
  • Is this right I'm practicing multiplying decimals by 10, 100, or 1,000
    11·1 answer
  • Write the equation y= x^2-6x+16 in vertex form
    6·1 answer
  • How can you use bar diagrams to compare quantities in real world situation
    13·1 answer
  • What is the standard deviation of the following data set rounded to the nearest tenth? 60, 40, 35, 45, 39
    14·1 answer
  • Use the distributive property to simplify: 4 (3m - 6)
    8·1 answer
  • Divisibility rules 3 6 and 9
    10·2 answers
  • A baseball player had 4 hits in 8 games. At this rate, how many hits will the baseball player have in the next 28 games?
    14·1 answer
  • The point is rotated 180 degrees using as the center. Explain why the image must lie on the ray. I need
    8·1 answer
  • Solve the equation 2x+3y=10 for y when you substitute in x = -4
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!